Navegação Ciências Exatas e da Terra por Autor "Metz, Fernando Lucas"
Resultados 1-16 de 16
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Analytic solution of the resolvent equations for heterogeneous random graphs : spectral and localization properties
Silva, Jeferson Dias da; Metz, Fernando Lucas (2022) [Artigo de periódico]The spectral and localization properties of heterogeneous random graphs are determined by the resolvent distributional equations, which have so far resisted an analytic treatment. We solve analytically the resolvent equations ... -
Analytic solution of the two-star model with correlated degrees
Bolfe, Maíra Angélica; Metz, Fernando Lucas; Guzmán-González, Edgar; Pérez-Castillo, Isaac (2021) [Artigo de periódico]Exponential random graphs are important to model the structure of real-world complex networks. Here we solve the two-star model with degree-degree correlations in the sparse regime. The model constraints the average ... -
Condensation of degrees emerging through a first-order phase transition in classical random graphs
Metz, Fernando Lucas; Pérez-Castillo, Isaac (2019) [Artigo de periódico]Due to their conceptual and mathematical simplicity, Erdös-Rényi or classical random graphs remain as a fundamental paradigm to model complex interacting systems in several areas. Although condensation phenomena have been ... -
Index statistical properties of sparse random graphs
Metz, Fernando Lucas; Stariolo, Daniel Adrian (2015) [Artigo de periódico]Using the replica method, we develop an analytical approach to compute the characteristic function for the probability PN(K,λ) that a large N × N adjacency matrix of sparse random graphs has K eigenvalues below a threshold ... -
Large-deviation theory for dilutedWishart random matrices
Pérez-Castillo, Isaac; Metz, Fernando Lucas (2018) [Artigo de periódico]Wishart random matrices with a sparse or diluted structure are ubiquitous in the processing of large datasets, with applications in physics, biology, and economy. In this work, we develop a theory for the eigenvalue ... -
Level compressibility for the Anderson model on regular random graphs and the eigenvalue statistics in the extended phase
Metz, Fernando Lucas; Pérez-Castillo, Isaac (2017) [Artigo de periódico]We calculate the level compressibility χ(W,L) of the energy levels inside [−L/2,L/2] for the Anderson model on infinitely large random regular graphs with on-site potentials distributed uniformly in [−W/2,W/2]. We show ... -
Linear stability analysis of large dynamical systems on random directed graphs
Neri, Izaak; Metz, Fernando Lucas (2020) [Artigo de periódico]We present a linear stability analysis of stationary states (or fixed points) in large dynamical systems defined on random, directed graphs with a prescribed distribution of indegrees and outdegrees. We obtain two remarkable ... -
Localization and universality of eigenvectors in directed random graphs
Metz, Fernando Lucas; Neri, Izaak (2021) [Artigo de periódico]Although the spectral properties of random graphs have been a long-standing focus of network theory, the properties of right eigenvectors of directed graphs have so far eluded an exact analytic treatment. We present a ... -
Mean-field theory of vector spin models on networks with arbitrary degree distributions
Metz, Fernando Lucas; Peron, Thomas (2022) [Artigo de periódico]Understanding the relationship between the heterogeneous structure of complex networks and cooperative phenomena occurring on them remains a key problem in network science. Mean-field theories of spin models on networks ... -
Pattern reconstruction and sequence processing in feed-forward layered neural networks near saturation
Metz, Fernando Lucas; Theumann, Walter Karl (2005) [Artigo de periódico]The dynamics and the stationary states for the competition between pattern reconstruction and asymmetric sequence processing are studied here in an exactly solvable feed-forward layered neural network model of binary units ... -
Period-two cycles in a feedforward layered neutral network model with symmetric sequence processing
Metz, Fernando Lucas; Theumann, Walter Karl (2007) [Artigo de periódico]The effects of dominant sequential interactions are investigated in an exactly solvable feedforward layered neural network model of binary units and patterns near saturation in which the interaction consists of a Hebbian ... -
Phase transitions in atypical systems induced by a condensation transition on graphs
Guzmán-González, Edgar; Pérez-Castillo, Isaac; Metz, Fernando Lucas (2020) [Artigo de periódico]Random graphs undergo structural phase transitions that are crucial for dynamical processes and cooperative behavior of models defined on graphs. In this work we investigate the impact of a first-order structural transition ... -
Spectral density of dense random networks and the breakdown of the Wigner semicircle law
Metz, Fernando Lucas; Silva, Jeferson Dias da (2020) [Artigo de periódico]Although the spectra of random networks have been studied for a long time, the influence of network topology on the dense limit of network spectra remains poorly understood. By considering the configuration model of networks ... -
Statistical properties of speckle patterns for a random number of scatterers and nonuniform phase distributions
Metz, Fernando Lucas; Bonatto, Cristian; Prado, Sandra Denise (2024) [Artigo de periódico]The statistical properties of speckle patterns have important applications in optics, oceanography, and transport phenomena in disordered systems. Here we obtain closed-form analytic results for the amplitude distribution ... -
Super rogue wave generation in the linear regime
Bonatto, Cristian; Prado, Sandra Denise; Metz, Fernando Lucas; Schoffen, Julio Ricardo; Correia, Ricardo Rego Bordalo; Hickmann, Jandir Miguel (2020) [Artigo de periódico]Extreme or rogue waves are large and unexpected waves appearing with higher probability than predicted by Gaussian statistics. Although their formation is explained by both linear and nonlinear wave propagation, nonlinearity ... -
Theory for the conditioned spectral density of noninvariant random matrices
Pérez-Castillo, Isaac; Metz, Fernando Lucas (2018) [Artigo de periódico]We develop a theoretical approach to compute the conditioned spectral density of N × N noninvariant random matrices in the limit N →∞. This large deviation observable, defined as the eigenvalue distribution conditioned to ...